%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:02:07 PM UTC 2026
% Result : Theorem 2.57s 1.30s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 33
% Syntax : Number of formulae : 213 ( 24 unt; 15 def)
% Number of atoms : 653 ( 14 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 829 ( 389 ~; 349 |; 55 &)
% ( 18 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 16 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 206 ( 0 sgn 202 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(growth_rate(X2,X3),growth_rate(X1,X3)) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(f3,axiom,
! [X0] :
( ( environment(X0)
& in_environment(X0,critical_point(X0)) )
=> subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(f4,axiom,
! [X0] :
( ( environment(X0)
& in_environment(X0,appear(efficient_producers,X0)) )
=> subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(f5,axiom,
! [X0] :
( ( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
& ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) )
=> decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( environment(X0)
& in_environment(X0,X2)
& greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater(X2,X1) )
=> ( decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
=> greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(f7,axiom,
! [X0] :
( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
<=> greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(f8,axiom,
! [X0] :
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
<=> greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& in_environment(X0,X1)
& in_environment(X0,X2)
& greater_or_equal(X2,X3)
& greater_or_equal(X3,X1) )
=> in_environment(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_durations_are_time_intervals) ).
fof(f12,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,critical_point(X0))
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater(critical_point(X0),X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(f14,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> subpopulations(efficient_producers,first_movers,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f15,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> greater_or_equal(X1,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(f16,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f17,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& ~ greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))) )
=> greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(f18,axiom,
! [X0,X1] :
( ( environment(X0)
& X1 = critical_point(X0) )
=> ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f19,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X3,X1)
& greater_or_equal(X2,X3) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10) ).
fof(f20,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
fof(f21,conjecture,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,critical_point(X0))
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater(critical_point(X0),X1) )
=> selection_favors(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& in_environment(X0,critical_point(X0))
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater(critical_point(X0),X1) )
=> selection_favors(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0)) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,appear(efficient_producers,X0)) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(X2,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0,X1,X2] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(X2,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( in_environment(X0,X3)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( in_environment(X0,X3)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0))
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0))
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f50,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3) ),
inference(ennf_transformation,[],[f19]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f54,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& environment(X0)
& in_environment(X0,critical_point(X0))
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater(critical_point(X0),X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f56,plain,
? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& environment(X0)
& in_environment(X0,critical_point(X0))
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater(critical_point(X0),X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
& ( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0] :
( ( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) )
& ( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f60,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
( ~ selection_favors(first_movers,efficient_producers,sK1)
& environment(sK0)
& in_environment(sK0,critical_point(sK0))
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& greater(critical_point(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f56]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| selection_favors(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f63,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f64,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f65,plain,
! [X0] :
( ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f32]) ).
fof(f67,plain,
! [X2,X0,X1] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f68,plain,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f57]) ).
fof(f70,plain,
! [X0] :
( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[],[f58]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| in_environment(X0,X3)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f75,plain,
! [X0,X1] :
( ~ environment(X0)
| in_environment(X0,X1)
| ~ in_environment(X0,critical_point(X0))
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f77,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f78,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f79,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f80,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f48]) ).
fof(f84,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(cnf_transformation,[],[f50]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f86,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f87,plain,
greater(critical_point(sK0),sK1),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(cnf_transformation,[],[f61]) ).
fof(f89,plain,
in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f61]) ).
fof(f90,plain,
environment(sK0),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f61]) ).
fof(f92,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f80]) ).
fof(f93,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[],[f84]) ).
fof(f96,plain,
! [X0] :
( ~ greater(zero,difference(growth_rate(first_movers,critical_point(X0)),growth_rate(efficient_producers,critical_point(X0))))
| ~ environment(X0) ),
inference(resolution,[],[f68,f93]) ).
fof(f99,plain,
! [X2,X0,X1] :
( in_environment(sK0,X0)
| ~ in_environment(sK0,X1)
| ~ in_environment(sK0,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X0,X1) ),
inference(resolution,[],[f72,f90]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in_environment(sK0,X0)
| ~ in_environment(sK0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sK0))
| ~ greater_or_equal(appear(efficient_producers,sK0),X0)
| ~ environment(sK0)
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(resolution,[],[f99,f65]) ).
fof(f102,plain,
! [X0,X1] :
( ~ in_environment(sK0,X0)
| ~ in_environment(sK0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sK0))
| ~ greater_or_equal(appear(efficient_producers,sK0),X0)
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(forward_subsumption_resolution,[],[f101,f90]) ).
fof(f104,definition,
( spl2_1
<=> subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f106,plain,
( subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl2_2
<=> ! [X1] :
( ~ in_environment(sK0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f109,plain,
( ! [X1] :
( ~ in_environment(sK0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sK0)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl2_3
<=> ! [X0] :
( ~ in_environment(sK0,X0)
| ~ greater_or_equal(appear(efficient_producers,sK0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f112,plain,
( ! [X0] :
( ~ greater_or_equal(appear(efficient_producers,sK0),X0)
| ~ in_environment(sK0,X0) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f102,f111,f108,f104]) ).
fof(f114,plain,
! [X2,X0,X1] :
( selection_favors(X0,X1,X2)
| ~ subpopulations(X1,X0,sK0,X2)
| ~ greater(growth_rate(X0,X2),growth_rate(X1,X2)) ),
inference(resolution,[],[f62,f90]) ).
fof(f115,plain,
( ~ greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0))
| ~ spl2_2 ),
inference(resolution,[],[f109,f89]) ).
fof(f119,plain,
! [X0] :
( in_environment(sK0,X0)
| ~ in_environment(sK0,critical_point(sK0))
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),X0) ),
inference(resolution,[],[f75,f90]) ).
fof(f122,plain,
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ spl2_2 ),
inference(resolution,[],[f115,f78]) ).
fof(f124,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f122,f90]) ).
fof(f129,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_2 ),
inference(resolution,[],[f124,f64]) ).
fof(f134,plain,
( ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f129,f90]) ).
fof(f143,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f134,f89]) ).
fof(f144,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f143]) ).
fof(f154,plain,
! [X0] :
( in_environment(sK0,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),X0) ),
inference(forward_subsumption_resolution,[],[f119,f89]) ).
fof(f155,plain,
( ~ in_environment(sK0,appear(efficient_producers,sK0))
| ~ spl2_3 ),
inference(resolution,[],[f112,f92]) ).
fof(f160,plain,
( ~ greater_or_equal(appear(efficient_producers,sK0),appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| ~ environment(sK0)
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(resolution,[],[f154,f65]) ).
fof(f161,plain,
( ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| ~ environment(sK0)
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(forward_subsumption_resolution,[],[f160,f92]) ).
fof(f163,plain,
( ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(forward_subsumption_resolution,[],[f161,f90]) ).
fof(f165,definition,
( spl2_8
<=> greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f167,plain,
( ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| spl2_8 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f168,plain,
( spl2_1
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f163,f165,f104]) ).
fof(f169,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0))
| spl2_8 ),
inference(resolution,[],[f167,f79]) ).
fof(f171,definition,
( spl2_9
<=> greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f173,plain,
( ~ greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0))
| spl2_9 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f175,definition,
( spl2_10
<=> critical_point(sK0) = appear(efficient_producers,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f177,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( ~ spl2_9
| spl2_10
| spl2_8 ),
inference(avatar_split_clause,[],[f169,f165,f175,f171]) ).
fof(f179,plain,
( ~ subpopulations(efficient_producers,first_movers,sK0,sK1)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(resolution,[],[f114,f91]) ).
fof(f181,definition,
( spl2_11
<=> greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f183,plain,
( ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| spl2_11 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f185,definition,
( spl2_12
<=> subpopulations(efficient_producers,first_movers,sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f187,plain,
( ~ subpopulations(efficient_producers,first_movers,sK0,sK1)
| spl2_12 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( ~ spl2_11
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f179,f185,f181]) ).
fof(f189,plain,
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| spl2_9 ),
inference(resolution,[],[f173,f78]) ).
fof(f191,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f189,f90]) ).
fof(f194,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,critical_point(sK0))
| spl2_9 ),
inference(resolution,[],[f191,f64]) ).
fof(f199,plain,
( ~ in_environment(sK0,critical_point(sK0))
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f194,f90]) ).
fof(f202,plain,
( $false
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f199,f89]) ).
fof(f203,plain,
spl2_9,
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f220,plain,
( ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_3
| ~ spl2_10 ),
inference(superposition,[],[f155,f177]) ).
fof(f226,plain,
( $false
| ~ spl2_3
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f220,f89]) ).
fof(f227,plain,
( ~ spl2_3
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[],[f226]) ).
fof(f244,definition,
( spl2_17
<=> ! [X0,X1] :
( ~ environment(X0)
| ~ greater(X1,sK1)
| ~ greater_or_equal(sK1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f245,plain,
( ! [X0,X1] :
( ~ environment(X0)
| ~ greater(X1,sK1)
| ~ greater_or_equal(sK1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(X0,X1) )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,definition,
( spl2_18
<=> decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f249,plain,
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| spl2_18 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f254,definition,
( spl2_19
<=> decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
fof(f256,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl2_20
<=> decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f259,plain,
( decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1)))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f260,plain,
( ~ decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1)))
| spl2_20 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f269,definition,
( spl2_22
<=> ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_22])],[avatar_definition]) ).
fof(f270,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) )
| spl2_20 ),
inference(resolution,[],[f260,f86]) ).
fof(f273,plain,
( spl2_22
| spl2_20 ),
inference(avatar_split_clause,[],[f272,f258,f269]) ).
fof(f274,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ spl2_22 ),
inference(resolution,[],[f270,f90]) ).
fof(f275,plain,
( ! [X0,X1] :
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(sK1,X0)
| ~ greater_or_equal(X1,sK1) )
| ~ spl2_22 ),
inference(resolution,[],[f274,f85]) ).
fof(f278,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(sK1,X0)
| ~ greater_or_equal(X1,sK1) )
| ~ spl2_22 ),
inference(forward_subsumption_resolution,[],[f275,f90]) ).
fof(f293,definition,
( spl2_26
<=> ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(X1,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_26])],[avatar_definition]) ).
fof(f294,plain,
( ! [X1] :
( ~ greater_or_equal(X1,sK1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f296,definition,
( spl2_27
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater_or_equal(sK1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_27])],[avatar_definition]) ).
fof(f297,plain,
( ! [X0] :
( ~ greater_or_equal(sK1,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( spl2_26
| spl2_27
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f278,f269,f296,f293]) ).
fof(f310,plain,
( ! [X0] :
( ~ greater(X0,sK1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) )
| ~ spl2_26 ),
inference(resolution,[],[f294,f81]) ).
fof(f313,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ spl2_26 ),
inference(resolution,[],[f310,f87]) ).
fof(f314,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_26 ),
inference(resolution,[],[f313,f64]) ).
fof(f319,plain,
( ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_26 ),
inference(forward_subsumption_resolution,[],[f314,f90]) ).
fof(f322,plain,
( $false
| ~ spl2_26 ),
inference(forward_subsumption_resolution,[],[f319,f89]) ).
fof(f323,plain,
~ spl2_26,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f326,plain,
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| spl2_12 ),
inference(resolution,[],[f187,f77]) ).
fof(f327,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| spl2_12 ),
inference(forward_subsumption_resolution,[],[f326,f90]) ).
fof(f328,plain,
( ! [X0,X1] :
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(sK1,X0)
| ~ greater_or_equal(X1,sK1) )
| spl2_12 ),
inference(resolution,[],[f327,f85]) ).
fof(f330,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(sK1,X0)
| ~ greater_or_equal(X1,sK1) )
| spl2_12 ),
inference(forward_subsumption_resolution,[],[f328,f90]) ).
fof(f331,plain,
( spl2_26
| spl2_27
| spl2_12 ),
inference(avatar_split_clause,[],[f330,f185,f296,f293]) ).
fof(f339,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| ~ spl2_27 ),
inference(resolution,[],[f297,f88]) ).
fof(f343,plain,
( $false
| ~ spl2_1
| ~ spl2_27 ),
inference(forward_subsumption_resolution,[],[f339,f106]) ).
fof(f344,plain,
( ~ spl2_1
| ~ spl2_27 ),
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f346,plain,
( ~ greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| spl2_11 ),
inference(resolution,[],[f183,f70]) ).
fof(f350,plain,
( ! [X0,X1] :
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ greater_or_equal(sK1,appear(efficient_producers,X0))
| ~ greater(X1,sK1) )
| spl2_11 ),
inference(resolution,[],[f346,f67]) ).
fof(f358,plain,
( ! [X0] :
( ~ greater(X0,sK1)
| ~ greater_or_equal(sK1,appear(efficient_producers,sK0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ in_environment(sK0,X0) )
| ~ spl2_17 ),
inference(resolution,[],[f245,f90]) ).
fof(f359,plain,
( ! [X0] :
( ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ greater(X0,sK1)
| ~ in_environment(sK0,X0) )
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f358,f88]) ).
fof(f360,plain,
( ! [X0,X1] :
( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ in_environment(sK0,X0)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater(X0,sK1) )
| ~ spl2_17 ),
inference(resolution,[],[f359,f82]) ).
fof(f385,plain,
( ! [X0,X1] :
( ~ environment(X1)
| ~ in_environment(sK0,critical_point(X0))
| ~ subpopulations(first_movers,efficient_producers,X1,critical_point(X0))
| ~ greater(critical_point(X0),sK1)
| ~ environment(X0) )
| ~ spl2_17 ),
inference(resolution,[],[f360,f96]) ).
fof(f400,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(X0))
| ~ greater(critical_point(X0),sK1)
| ~ in_environment(sK0,critical_point(X0)) )
| ~ spl2_17 ),
inference(resolution,[],[f385,f90]) ).
fof(f424,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ greater(critical_point(sK0),sK1)
| ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_17 ),
inference(resolution,[],[f400,f90]) ).
fof(f425,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f424,f87]) ).
fof(f426,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f425,f89]) ).
fof(f427,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_17 ),
inference(resolution,[],[f426,f64]) ).
fof(f432,plain,
( ~ in_environment(sK0,critical_point(sK0))
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f427,f90]) ).
fof(f435,plain,
( $false
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f432,f89]) ).
fof(f436,plain,
~ spl2_17,
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f438,plain,
( spl2_17
| ~ spl2_18
| spl2_11 ),
inference(avatar_split_clause,[],[f350,f181,f247,f244]) ).
fof(f439,plain,
( ~ decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1)))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| spl2_18 ),
inference(resolution,[],[f249,f66]) ).
fof(f440,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| spl2_18
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f439,f259]) ).
fof(f441,plain,
( spl2_19
| spl2_18
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f440,f258,f247,f254]) ).
fof(f442,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) )
| ~ spl2_19 ),
inference(resolution,[],[f256,f63]) ).
fof(f443,plain,
( spl2_22
| ~ spl2_19 ),
inference(avatar_split_clause,[],[f442,f254,f269]) ).
cnf(s1,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f144]) ).
cnf(s5,plain,
( spl2_1
| ~ spl2_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s6,plain,
( spl2_8
| ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f178]) ).
cnf(s7,plain,
( ~ spl2_11
| ~ spl2_12 ),
inference(sat_conversion,[],[f188]) ).
cnf(s9,plain,
spl2_9,
inference(sat_conversion,[],[f203]) ).
cnf(s12,plain,
( ~ spl2_3
| ~ spl2_10 ),
inference(sat_conversion,[],[f227]) ).
cnf(s18,plain,
( spl2_20
| spl2_22 ),
inference(sat_conversion,[],[f273]) ).
cnf(s20,plain,
( ~ spl2_22
| spl2_26
| spl2_27 ),
inference(sat_conversion,[],[f298]) ).
cnf(s23,plain,
~ spl2_26,
inference(sat_conversion,[],[f323]) ).
cnf(s26,plain,
( spl2_12
| spl2_26
| spl2_27 ),
inference(sat_conversion,[],[f331]) ).
cnf(s29,plain,
( ~ spl2_1
| ~ spl2_27 ),
inference(sat_conversion,[],[f344]) ).
cnf(s42,plain,
~ spl2_17,
inference(sat_conversion,[],[f436]) ).
cnf(s44,plain,
( spl2_11
| spl2_17
| ~ spl2_18 ),
inference(sat_conversion,[],[f438]) ).
cnf(s45,plain,
( spl2_18
| spl2_19
| ~ spl2_20 ),
inference(sat_conversion,[],[f441]) ).
cnf(s46,plain,
( ~ spl2_19
| spl2_22 ),
inference(sat_conversion,[],[f443]) ).
cnf(s49,plain,
( ~ spl2_22
| spl2_27 ),
inference(rat,[],[s20,s23]) ).
cnf(s51,plain,
( spl2_8
| spl2_10 ),
inference(rat,[],[s6,s9]) ).
cnf(s52,plain,
( spl2_1
| spl2_3 ),
inference(rat,[],[s1,s3]) ).
cnf(s53,plain,
spl2_1,
inference(rat,[],[s12,s51,s52,s5]) ).
cnf(s54,plain,
~ spl2_27,
inference(rat,[],[s29,s53]) ).
cnf(s55,plain,
spl2_12,
inference(rat,[],[s26,s23,s54]) ).
cnf(s56,plain,
~ spl2_22,
inference(rat,[],[s49,s54]) ).
cnf(s57,plain,
~ spl2_11,
inference(rat,[],[s7,s55]) ).
cnf(s58,plain,
~ spl2_19,
inference(rat,[],[s46,s56]) ).
cnf(s59,plain,
spl2_20,
inference(rat,[],[s18,s56]) ).
cnf(s60,plain,
~ spl2_18,
inference(rat,[],[s44,s42,s57]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s45,s58,s59,s60]) ).
fof(f444,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:22:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.57/1.30 % (3285983)Detected formulas, will run a generic FOF schedule.
% 2.57/1.30 % (3285989)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2287085700:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.30 % (3285992)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1064780754:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.30 % (3285994)dis-21_1_sil=8000:lcm=predicate:random_seed=150007417:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.57/1.30 % (3285991)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3560815925:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.30 % (3285990)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=813081717:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.30 % (3285988)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=164596332:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.30 % (3285993)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1833602161:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.30 % (3285993)First to succeed.
% 2.57/1.30 % (3285993)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3285983"
% 2.57/1.30 % (3285991)Instruction limit reached!
% 2.57/1.30 % (3285991)------------------------------
% 2.57/1.30 % (3285991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.30 % (3285991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.30 % (3285991)CaDiCaL version: 2.1.3
% 2.57/1.30 % (3285991)Termination reason: Instruction limit
% 2.57/1.30 % (3285991)Termination phase: Saturation
% 2.57/1.30 % (3285991)Time elapsed: 0.063 s
% 2.57/1.30 % (3285991)Peak memory usage: 89 MB
% 2.57/1.30 % (3285991)Instructions burned: 110 (million)
% 2.57/1.30 % (3285992)Instruction limit reached!
% 2.57/1.30 % (3285992)------------------------------
% 2.57/1.30 % (3285992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.30 % (3285992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.30 % (3285992)CaDiCaL version: 2.1.3
% 2.57/1.30 % (3285992)Termination reason: Instruction limit
% 2.57/1.30 % (3285992)Termination phase: Saturation
% 2.57/1.30 % (3285992)Time elapsed: 0.065 s
% 2.57/1.30 % (3285992)Peak memory usage: 88 MB
% 2.57/1.30 % (3285992)Instructions burned: 120 (million)
% 2.57/1.30 % (3285994)Instruction limit reached!
% 2.57/1.30 % (3285994)------------------------------
% 2.57/1.30 % (3285994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.30 % (3285994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.30 % (3285994)CaDiCaL version: 2.1.3
% 2.57/1.30 % (3285994)Termination reason: Instruction limit
% 2.57/1.30 % (3285994)Termination phase: Saturation
% 2.57/1.30 % (3285994)Time elapsed: 0.080 s
% 2.57/1.30 % (3285994)Peak memory usage: 89 MB
% 2.57/1.30 % (3285994)Instructions burned: 130 (million)
% 2.57/1.30 % (3286002)lrs+10_1_sil=8000:sp=occurrence:random_seed=911532488:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.57/1.30 % (3286003)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2525250704:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.57/1.30 % (3286003)Refutation not found, incomplete strategy
% 2.57/1.30 % (3286003)------------------------------
% 2.57/1.30 % (3286003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.30 % (3286003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.30 % (3286003)CaDiCaL version: 2.1.3
% 2.57/1.30 % (3286003)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.30 % (3286003)Time elapsed: 0.002 s
% 2.57/1.30 % (3286003)Peak memory usage: 88 MB
% 2.57/1.30 % (3286003)Instructions burned: 2 (million)
% 2.57/1.30 % (3286004)lrs+1011_1_sil=32000:sp=occurrence:random_seed=28624662:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.57/1.30 % (3286004)Also succeeded, but the first one will report.
% 2.57/1.30 % (3285993)Refutation found. Thanks to Tanya!
% 2.57/1.30 % SZS status Theorem for theBenchmark
% 2.57/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.39 % (3285993)------------------------------
% 3.59/1.39 % (3285993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.39 % (3285993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.39 % (3285993)CaDiCaL version: 2.1.3
% 3.59/1.39 % (3285993)Termination reason: Refutation
% 3.59/1.39 % (3285993)Time elapsed: 0.015 s
% 3.59/1.39 % (3285993)Peak memory usage: 89 MB
% 3.59/1.39 % (3285993)Instructions burned: 18 (million)
% 3.59/1.39 % (3285993)------------------------------
% 3.59/1.39 % (3285993)------------------------------
% 3.59/1.39 % (3285983)Success in time 0.446 s
% 3.59/1.39 % Vampire exiting
%------------------------------------------------------------------------------